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class sklearn.manifold.LocallyLinearEmbedding(n_neighbors=5, n_components=2, reg=0.001, eigen_solver='auto', tol=1e-06, max_iter=100, method='standard', hessian_tol=0.0001, modified_tol=1e-12, neighbors_algorithm='auto', random_state=None, n_jobs=1)
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Locally Linear Embedding
Read more in the User Guide.
Parameters: n_neighbors : integer
number of neighbors to consider for each point.
n_components : integer
number of coordinates for the manifold
reg : float
regularization constant, multiplies the trace of the local covariance matrix of the distances.
eigen_solver : string, {?auto?, ?arpack?, ?dense?}
auto : algorithm will attempt to choose the best method for input data
- arpack
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For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results.
- dense
: use standard dense matrix operations for the eigenvalue
decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems.
tol : float, optional
Tolerance for ?arpack? method Not used if eigen_solver==?dense?.
max_iter : integer
maximum number of iterations for the arpack solver. Not used if eigen_solver==?dense?.
method : string (?standard?, ?hessian?, ?modified? or ?ltsa?)
- standard
: use the standard locally linear embedding algorithm. see
reference [1]
hessian
: use the Hessian eigenmap method. This method requires
n_neighbors > n_components * (1 + (n_components + 1) / 2
see reference [2]
modified
: use the modified locally linear embedding algorithm.
see reference [3]
ltsa
: use local tangent space alignment algorithm
see reference [4]
hessian_tol : float, optional
Tolerance for Hessian eigenmapping method. Only used if method == 'hessian'
modified_tol : float, optional
Tolerance for modified LLE method. Only used if method == 'modified'
neighbors_algorithm : string [?auto?|?brute?|?kd_tree?|?ball_tree?]
algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance
random_state: numpy.RandomState or int, optional :
The generator or seed used to determine the starting vector for arpack iterations. Defaults to numpy.random.
n_jobs : int, optional (default = 1)
The number of parallel jobs to run. If -1
, then the number of jobs is set to the number of CPU cores.
Attributes:
embedding_vectors_ : array-like, shape [n_components, n_samples]
Stores the embedding vectors
reconstruction_error_ : float
Reconstruction error associated with embedding_vectors_
nbrs_ : NearestNeighbors object
Stores nearest neighbors instance, including BallTree or KDtree if applicable.
References
[R186] | Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000). |
[R187] | Donoho, D. & Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci U S A. 100:5591 (2003). |
[R188] |
Zhang, Z. & Wang, J. MLLE: Modified Locally Linear Embedding Using Multiple Weights. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382
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[R189] | Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004) |
Methods
fit (X[, y]) | Compute the embedding vectors for data X |
fit_transform (X[, y]) | Compute the embedding vectors for data X and transform X. |
get_params ([deep]) | Get parameters for this estimator. |
set_params (\*\*params) | Set the parameters of this estimator. |
transform (X) | Transform new points into embedding space. |
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__init__(n_neighbors=5, n_components=2, reg=0.001, eigen_solver='auto', tol=1e-06, max_iter=100, method='standard', hessian_tol=0.0001, modified_tol=1e-12, neighbors_algorithm='auto', random_state=None, n_jobs=1)
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fit(X, y=None)
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Compute the embedding vectors for data X
Parameters: X : array-like of shape [n_samples, n_features]
training set.
Returns: self : returns an instance of self.
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fit_transform(X, y=None)
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Compute the embedding vectors for data X and transform X.
Parameters: X : array-like of shape [n_samples, n_features]
training set.
Returns: X_new: array-like, shape (n_samples, n_components) :
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get_params(deep=True)
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Get parameters for this estimator.
Parameters: deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params : mapping of string to any
Parameter names mapped to their values.
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set_params(**params)
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Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it?s possible to update each component of a nested object.Returns: self :
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transform(X)
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Transform new points into embedding space.
Parameters: X : array-like, shape = [n_samples, n_features] Returns: X_new : array, shape = [n_samples, n_components] Notes
Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs)
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